I propose in this thread that the Knight of the Laughing Tree was Howland Reed skinchanged by Bran. Shout out to @LynnS for making a thread earlier about the Knight of the Laughing Tree identity. This is just a theory and I am not sure if its correct or not
How did Howland Reed actually defeat the knights? Well the gods helped him:
"Whoever he was, the old gods gave strength to his arm."
"And so the little crannogman's prayer was answered . . . by the green men, or the old gods, or the children of the forest, who can say?"
The strength came from Bran, the Old Gods, skinchanging Howland Reed. We can observe this in Hodor when Bran skinchanges him and Hodor is able to to do things that he was not able to before:
"HOOOOOODOOOOOOOR!" the stableboy screamed as lightning filled the sky again, and even Jojen was shouting now, shouting at Bran and Meera to shut him up.
"Be quiet!" Bran said in a shrill scared voice, reaching up uselessly for Hodor's leg as he crashed past, reaching, reaching.
Hodor staggered, and closed his mouth. He shook his head slowly from side to side, sank back to the floor, and sat crosslegged. When the thunder boomed, he scarcely seemed to hear it. The four of them sat in the dark tower, scarce daring to breathe.
"Hoooodor" came a whimper, from somewhere down below.
And suddenly he was not Bran, the broken boy crawling through the snow, suddenly he was Hodor halfway down the hill, with the wight raking at his eyes. Roaring, he came lurching to his feet, throwing the thing violently aside. It went to one knee, began to rise again. Bran ripped Hodor's longsword from his belt. Deep inside he could hear poor Hodor whimpering still, but outside he was seven feet of fury with old iron in his hand. He raised the sword and brought it down upon the dead man, grunting as the blade sheared through wet wool and rusted mail and rotted leather, biting deep into the bones and flesh beneath. "HODOR!" he bellowed, and slashed again. This time he took the wight's head off at the neck, and for half a moment he exulted … until a pair of dead hands came groping blindly for his throat.
Howland did pray for the for the old gods to give him strength:
but before he slept he knelt on the lakeshore, looking across the water to where the Isle of Faces would be, and said a prayer to the old gods of north and Neck . . .
Bran does answer prayers:
"Father." Bran's voice was a whisper in the wind, a rustle in the leaves. "Father, it's me. It's Bran. Brandon."
Eddard Stark lifted his head and looked long at the weirwood, frowning, but he did not speak. He cannot see me, Bran realized, despairing. He wanted to reach out and touch him, but all that he could do was watch and listen. I am in the tree. I am inside the heart tree, looking out of its red eyes, but the weirwood cannot talk, so I can't.
Eddard Stark resumed his prayer. Bran felt his eyes fill up with tears. But were they his own tears, or the weirwood's? If I cry, will the tree begin to weep?
Lord Eddard Stark sat upon a rock beside the deep black pool in the godswood, the pale roots of the heart tree twisting around him like an old man's gnarled arms. The greatsword Ice lay across Lord Eddard's lap, and he was cleaning the blade with an oilcloth.
"Winterfell," Bran whispered.
His father looked up. "Who's there?" he asked, turning …
Theon found himself wondering if he should say a prayer. Will the old gods hear me if I do? They were not his gods, had never been his gods. He was ironborn, a son of Pyke, his god was the Drowned God of the islands … but Winterfell was long leagues from the sea. It had been a lifetime since any god had heard him. He did not know who he was, or what he was, why he was still alive, why he had ever been born.
"Theon," a voice seemed to whisper.
A leaf drifted down from above, brushed his brow, and landed in the pool. It floated on the water, red, five-fingered, like a bloody hand. "… Bran," the tree murmured.
They know. The gods know. They saw what I did. And for one strange moment it seemed as if it were Bran's face carved into the pale trunk of the weirwood, staring down at him with eyes red and wise and sad. Bran's ghost, he thought, but that was madness. Why should Bran want to haunt him? He had been fond of the boy, had never done him any harm.
Bran is able to see the past in the weirwood and affect the past. We know this, because of Hodor's condition. Edit: What I mean by the "past" is the past that is current timeline. Bran cannot affect the timeline and the wierwoods do not have past or future. Bran was more akin to being "present" in Harrenhal. He certainly cannot affect anything currently. From what I know.
Here's the passage of when Varamyr dies, he is able to warg his wolf from the weirwood:
When he tried to scream, she spat their tongue out.
The white world turned and fell away. For a moment it was as if he were inside the weirwood, gazing out through carved red eyes as a dying man twitched feebly on the ground and a madwoman danced blind and bloody underneath the moon, weeping red tears and ripping at her clothes. Then both were gone and he was rising, melting, his spirit borne on some cold wind. He was in the snow and in the clouds, he was a sparrow, a squirrel, an oak. A horned owl flew silently between his trees, hunting a hare; Varamyr was inside the owl, inside the hare, inside the trees. Deep below the frozen ground, earthworms burrowed blindly in the dark, and he was them as well. I am the wood, and everything that's in it, he thought, exulting. A hundred ravens took to the air, cawing as they felt him pass. A great elk trumpeted, unsettling the children clinging to his back. A sleeping direwolf raised his head to snarl at empty air. Before their hearts could beat again he had passed on, searching for his own, for One Eye, Sly, and Stalker, for his pack. His wolves would save him, he told himself.
That was his last thought as a man.
As to why would Bran go to Harrenhal? Well, from Bloodraven's quote, he has been watching Ned and saw Bran's birth, and that Bran is a one in a thousand. I think it was very important for Bran to be born. During the Harrenhal tourney, Catelyn was supposed to marry Brandon, if she did marry Brandon then Bran would not be born. So he had to interfere to make sure he was born:
"Only one man in a thousand is born a skinchanger," Lord Brynden said one day, after Bran had learned to fly, "and only one skinchanger in a thousand can be a greenseer."
I have watched you for a long time, watched you with a thousand eyes and one. I saw your birth, and that of your lord father before you. I saw your first step, heard your first word, was part of your first dream. I was watching when you fell. And now you are come to me at last, Brandon Stark, though the hour is late."
"Will this make me a greenseer?"
"Your blood makes you a greenseer," said Lord Brynden. "This will help awaken your gifts and wed you to the trees."
Also, Bran had always wanted to be a knight and this was his chance:
One day I will be like him. The thought filled Bran with dread. Bad enough that he was broken, with his useless legs. Was he doomed to lose the rest too, to spend all of his years with a weirwood growing in him and through him? Lord Brynden drew his life from the tree, Leaf told them. He did not eat, he did not drink. He slept, he dreamed, he watched. I was going to be a knight, Bran remembered. I used to run and climb and fight. It seemed a thousand years ago.
What was he now? Only Bran the broken boy, Brandon of House Stark, prince of a lost kingdom, lord of a burned castle, heir to ruins. He had thought the three-eyed crow would be a sorcerer, a wise old wizard who could fix his legs, but that was some stupid child's dream, he realized now. I am too old for such fancies, he told himself. A thousand eyes, a hundred skins, wisdom deep as the roots of ancient trees. That was as good as being a knight. Almost as good, anyway.